42. A teacher wants to examine the effect of frequent quizzes on retention of class material. In one of her sections, she gives 5 quizzes throughout the semester. In the other section, she only has two large exams. At the end of the semester, a test of overall statistics knowledge is given to all students. Below are the summary statistics for both sections.

Two Exams Frequent Quizzes

n = 25 n = 36

x = 78 x =82

s = 2.65 s = 2.83

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Using an independent-samples t-test, indicate whether the two classes result in significantly different amounts of knowledge retained. Use the .01 level of significance.(questions 42-46)

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Which of the following accurately represents the null and alternative hypotheses?(MUST SHOW WORK FOR THIS QUESTION)

a. H₀: 11- 22 == 0

H₁: 11- 220

b. H₀:x₁- x₂ == 0

H₁:x₁- x₂ 0

c. H₀:x₁- x₂ 0

H₁:x₁- x₂ >>0

d. H₀:11- 22 0

H₁: 11- 22 << 0

43. Which of the followingrepresents the propercritical region(MUST SHOW WORK FOR THIS PROBLEM).

a. 2.70

b. 2.75

c. 2.70

d. 2.75

44. Compute the test statistics (t-obs).(MUST SHOW WORK FOR THIS PROBLEM).

45. Based on the calculated test statistic,would you reject the null hypothesis established in question 42(MUST SHOW WORK FOR THIS PROBLEM)?

a. yes

b. no

46. Based on the previously conducted steps we can conclude that (MUST SHOW WORK FOR THIS PROBLEM):

a. There is a significant difference in knowledge retained between the two classes

b. There is no significant difference in knowledge retained between the two classes

c. The "two exams" class retained significantly less knowledge compared to the "frequent quizzes"class

d. The "frequent quizzes" class retained significantly more knowledge compared to the "two exams" class